A Computer Program for Aircraft Balancing

Pavlin S., Rogulji} S.: Ra~unalni{ki program za uravnote`enje - A Computer Program for Balancing

Uravnoteženje letala je zelo odgovorno delo za varnost letala v letenju in pristajanju. Navadno se uravnoteženje letala izdeluje na diagramih zraènih prevoznikov, ki niso poenoteni. V naèrtovanem èasu sprejema in odpreme letala zahteva uravnoteženje letala veliko hitrost in natanènost. Program za nadzor sprejema, odpreme in uravnoteženje letala je izdelan na letališèu Split, ki je v skladu s standardi Mednarodnega združenja zraènih prevoznikov, definiranih v dokumentu Priroènik za letališki sprejem in odpremo. Program je uspešno uporabljen na letališèih: Split, Dubrovnik, Pulj, Zadar, Osijek in Knock na Irskem za zraène prevoznike in tipe letal, ki pristajajo na teh letališèih in za zraènega prevoznika Air Zimbabwe. Rezultat novega postopka pri raèunalniškem programm za uravnoteženje letala je univerzalni program, ki ustreza floti katerega koli zraènega prevoznika. Raèunalniški program so preskusili in odobrili zraèni prevozniki: Croatia Airlines, Adria Airways, Austrian Airlines, ÈSA, LOT, Malev, Lauda Air, Air Loyd, Fischer Air, Condor in Duo Airways.

© 2004 Strojniški vestnik. Vse pravice pridržane.

(Kljuène besede: letala, varnost, uravnoteženje, programi raèunalniški)

Aircraft balancing is an activity of great responsibility for the safety of aircraft in flying and landing. Usually aircraft balancing is made on air-carrier diagrams that are not unified. Regarding the planned total aircraft handling time, aircraft balancing requires great speed and, at the same time, great accuracy. A program has been developed at Airport Split for ramp handling control and aircraft balancing that fully complies with the standards defined in the International Air Transport Association document Airport Handling Manual. The program has been succesfully implemented at the following airports: Split, Dubrovnik, Pula, Zadar, Osijek and Knock (in Ireland) for air carriers and aircraft fleet landing at those airports, as well as the air carrier Air Zimbabwe. The new approach to the computer program for aircraft balancing resulted in a universal program able to correspond with any air-carrier fleet. This computer program has been tested and approved by the following air carriers: Croatia Airlines, Adria Airways, Austrian Airlines, CSA, LOT, Malev, Lauda Air, Air Loyd, Fischer Air, Condor and Duo Airways.

© 2004 Journal of Mechanical Engineering. All rights reserved.

(Keywords:aircraft, safety, balancing, computer programs)

A Computer Program for Aircraft Balancing

Stanislav Pavlin - Slavko Rogulji}

Pregledni znanstveni ~lanek (1.02) Review scientific paper (1.02)

Ra~unalni{ki program za uravnote`enje

letala

0 UVOD

Uravnoteženje letala je preraèun mase letala in lege težišèa letala z optimalno razporejenimi potniki, prtljago in tovorom. Zaposleni na sprejemu in odpremi letala in uravnoteženje morajo poznati standarde, ki jih zahteva zraèni prevoznik za doloèen tip letala, glavne karakteristike letala in omejitve mase letala. To pomeni, da mora nadzornik sprejema in odpreme letala odloèiti o razporedu potnikov, prtljage in tovora v letalu o podatkih o številu in masi

0 INTRODUCTION

potnikov, prostornini in masi prtljage in tovora in trajanju leta [1]. Težišèe mora biti znotraj doloèenih mejnih vrednosti, ki omogoèajo letalu varno letenje in pristajanje [2].

1 MASE LETALA IN PRERAÈUN TEŽIŠÈA PRAZNEGA IN NATOVORJENEGA

LETALA

Za vsako letalo obstajajo omejitve mase zaradi aerodinamiène stabilnosti in strukturne nosilnosti. Razlikujejo se: najveèja projektirana masa (na vozni stezi, pri vzletanju, brez goriva, pri pristajanju), najveèja dovoljena masa (odvisno od fiziènih karakteristik letališèa kot so nadmorska višina, nagib vzletno-pristajalne steze in dolžina, ovire,smer in moè vetra, temperatura itn.), operativne mase (prazna po proizvajalcu, osnovna, suha operativna, operativna), in dejanske mase (pri vzletanju, pri pristajanju, brez goriva, na vozni stezi) [3].

Za preraèun težišèa praznega in natovorjenega letala se uporabljajo naslednje metode: - analitièna,

- grafièna in - indeksna.

1.1 Analitièna metoda

Za prazno ali naloženo letalo se lahko izraèuna lega težišèa z uporabo analitiène metode. Z drugimi besedami, znotraj doloèenega koordinatnega sistema se raèunajo momenti vseh komponent in delijo z maso teh komponent. Ker je moment sile enak sila krat roèica, se lahko tako izraèuna roèica, na katerem deluje rezultantna sila [1].

Za prazno letalo se izraèuna masa vsakega posameznega dela, vgrajenega v letalo, ali dela, ki je v njem, in natanèna lega vsakega dela. Seštevek vseh momentov, deljen s skupno maso, da lego težišèa.

Masa vsakega dela letala deluje na ustrezni roèici osi x (npr. Gm na Xm) in iz tega izhaja, da je:

Ker je letalo sestavljeno iz številnih sestavnih delov, analitièna metoda uporablja tako imenovani produkcijski prerez namesto osi z, in os letala namesto osi x.

V primeru naloženega letala in znane mase praznega letala in lege težišèa praznega letala se uporablja enaka metoda za izraèun

passengers, the volume and weight of the baggage and the cargo, and the aircraft flight duration, the aircraft load controller has to make a decision about the arrangement of passengers, baggage and cargo in the aircraft [1]. The center of gravity must be within specified limits which allows aircraft safety in flying and landing [2].

1 AIRCRAFT WEIGHTS AND CALCULATING THE CENTRE OF GRAVITY OF EMPTY AND

LOADED AIRCRAFT

There are limits to the weight of every air-craft, both because of aerodynamic stability and be-cause of structural strength. These limits are as fol-lows: Maximum Design Weights (taxi, take off, zero fuel and landing), Maximum Allowed Weights (de-pends on the physical characteristics of the airport, like altitude, runway gradient and length, obstacles, wind direction and power, temperature; Operating Weights (manufacturer empty, basic, dry operating, operating); and Actual Weights (take off, landing, zero fuel, taxi)[3].

In calculating the centre of gravity of an empty and a loaded aircraft the following methods are used:

- the analytical method, - the graphical method, and - the index method.

1.1 Analytical method

For an empty or loaded aircraft the point of gravitation force, i.e., the centre of gravity, can be determined by the analytical method. In other words, the moments of all the components are calculated within a certain coordinate system and divided by the weights of these components. Since the moment of force equals force x length, it is in this way that the length is obtained at which the resulting force is acting [1].

Thus, the weight for every single part installed or located in the aircraft needs to be calculated for an empty aircraft, as well as the exact location of every single part. The sum of all the moments divided by the total weight (of all the parts) will yield the position of the centre of gravity.

The weight of every part of the aircraft acts at a certain lenght of the x axis (e.g. Gm at Xm), and therefore:

(1).

Since an aircraft consists of numerous components, the analytical method uses the so-called Manufacturer zero Station instead of the z axis, and the Centre Line instead of the x axis.

In the case of a loaded aircraft, with the known weight of the empty aircraft as well as the position of the centre of gravity of the empty aircraft, the same method is

1

1 n

i i i A n

i i

G X X

G

=

=

=

å

težišèa za vsakega potnika, blago ali prtljago. Vsak natovorjeni kilogram na doloèenem mestu v letalu prispeva k premiku težišèa.

Sledi:

Ga= masa praznega letala

G1= masa tovora

Gp= masa potnikov

G2= masa tovora

1.2 Grafièna metoda

Grafièna metoda se razlikuje od analitiène tako, da je raèunanje zamenjano z risanjem. Za vsako komponento se nariše premik težišèa letala v smeri nosa ali repa letala v odvisnosti od lege in mase tovora. Primer izraèuna težišèa letala z analitièno metodo bi bil pri grafièni metodi videti kakor na sliki 2.

Prazno letalo ima težišèe v Xa. Izraèuna se masa potnikov in dobi premik težišèa v toèko Xap, ki ustreza težišèu za maso letala + maso potnikov. Nadaljnji premik je odvisen od mase tovora G2 in G1 in težišèe se premika v toèko Xc.g.,

used to calculate the centre of gravity for every passenger, item of goods or baggage. Thus, every loaded kilogram at a certain position within the aircraft will affect the shift of the final point of gravitation force, i.e., the centre of gravity. It follows that:

(2),

Ga= weight of empty aircraft

G1= weight of cargo

Gp= weight of passengers

G2= weight of cargo

1.2 Graphical method

The graphical method differs from the analytical method in that it uses drawings instead of calculations. In other words, the shift of the centre of gravity is entered for every component towards the aircraft nose or tail, and depending on the position and weight of the loaded cargo. Thus, as an example of a calculation of the centre of gravity of an aircraft using the analytical method, the application of the graphical method would be as in Figure 2.

The empty aircraft has its centre of gravity at Xa. If the weight of the passengers Gp is calculated, this will yield a shift of the centre of gravity to the point Xap, which corresponds to the point of aircraft weight +

Sl. 1. Izraèun težišèa z analitièno metodo

Fig. 1. The centre-of-gravity calculation using the analytical method

1 1 2 2 . .

1 2

A A p p

c g

A p

G X G X G X G X

X

G G G G

+ + +

=

+ + +

Sl. 2. Izraèun težišèa z grafièno metodo

kar ustreza težišèu praznega letala, tovora in vkrcanih potnikov. Torej je premik težišèa zmeraj odvisen od mase in lege tovora in vkrcanih potnikov [1]. Izraèun težišèa se z razdelitvijo letala poenostavi na sekcije (npr. potniška kabina – sekcija A, B, C in prtljažni prostori 1 in 2), tovor pa se raèuna po sekcijah in premika težišèe na raèun tovora v posamezni sekciji na pripravljeni lestvici (sl. 2).

1.3 Indeksna metoda

Ker se pri uravnoteženju letala z analitièno metodo uporabljajo decimalna števila in razliène merske enote in so mogoèe napake pri izraèunu, je uveden pojem indeks kot spremenjeni moment (številka pomeni moment), ki skupaj z maso letala doloèi težišèe:

Temeljni indeks

kjer so:

- A in B – stalnice, ki zavarujejo, da se vrednost indeksa giblje znotraj doloèenih obmoèij;

- XRL – dolžina od proizvajalèevega prereza (Ø STA)

do referenène èrte ali indeksne èrte;

- Xc.g. – dolžina od proizvajalèevega prereza do težišèa

praznega letala;

- G – masa praznega letala (basic weight).

passengers weight. In the same way a further shift depends on the weight of cargo G2 and G1, so that the centre of

gravity is further moved to the point Xc.g., which corresponds to the point of force for the empty aircraft plus the value of the loaded cargo and passengers. Thus, the shift of the centre of gravity depends always on the weight and the position of the loaded cargo and passengers [1]. The calculation of the aircraft’s centre of gravity using the graphical method is still further simplified by dividing the aircraft into sections (e.g. passenger cabin - sections A, B, C and cargo compartments 1 and 2), so that cargo is calculated per section and the shift of the centre of gravity considering the cargo in a certain section on a prepared scale (Figure 2).

1.3 Index method

Since decimal numbers and different measuring units are often used when calculating the aircraft balance with the analytical method, resulting in possible errors of calculation, the term index has been introduced as the transformed moment (the number which represents moment), which together with the aircraft weight determines the centre of gravity: Basic Index

(3),

where:

- A and B are constants which ensure that the index value remains within certain limits;

- XRL is the length from the manufacturer’s cross

section (Ø STA) to the reference line or index line; - X c.g. is the length from the manufacturer’s cross

section to the centre of gravity of an empty aircraft; - G is the weight of an empty aircraft (Basic Weight).

. .

(XRL Xc g)G BI A

B =

-Sl. 3. Uravnoteženje letala z indeksno metodo

Èe se namesto osnovne mase v enaèbo, da vrednost suhe operativne mase (SOM - D.O.W.) z ustrezajoèo lego težišèa letala, tedaj se kot rezultat dobi suhi operativni indeks (SOI - D.O.I.) (sl. 3).

Èe se prazno letalo, za katerega je izraèunan osnovni ali suhi operativni indeks, želi obremeniti in uravnotežiti, se mora popraviti vrednost indeksa: nov indeks = indeks praznega letala + popravni indeks ali I (natovorjeni 0 D. O. I. + DI), in popravni indeks je:

kjer so:

B – stalnica, enaka kakor za izraèun osnovnega indeksa;

Xrl – oddaljenost od proizvajalèevega prereza do indeksne ali referenène èrte;

Xt – oddaljenost težišèa tovora (ki je natovorjen v letalo) od proizvajalèevega prereza;

Gt – masa nakladanega tovora.

Rezultati za osnovni indeks (za vsak tip letala posebej) so standardni, vsak zraèni prevoznik jih doloèi zase. Vrednost suhe operativne mase je odvisna od števila in mase èlanov posadke, mase hrane in pijaèe za potnike in posadko, mase blaga v brezcarinski prodaji. Vse to je prikazano razpredelnièno [1].

Referenèna ali indeksna èrta se lahko postavi kjerkoli v letalu (odvisno od tega, za kateri tovor se želi odstraniti velik vpliv rezultirajoèega momenta ali indeksa), tako da so za isti tip letala lahko vrednosti indeksa razliène.

2 POMANJKLJIVOSTI SEDANJIH PROGRAMOV ZA URAVNOTEŽENJE LETALA

Zraèni prevozniki imajo lastne sisteme za uravnoteženje letala. Podobni programi so bili razviti izkljuèno za velike zraène prevoznike: to so Lufthansa, British Airways, Swisair, Delta za njihove potrebe v skladu z njihovimi kriteriji in standardi. Ti prevozniki so prodajali programe drugim zraènim prevoznikom in jim dali programsko podporo. Pred približno desetimi leti so se prevozniki izogibali uporabi grafiène podpore zaradi potrebnega velikega pomnilnika, razmeroma majhne hitrosti in zmogljivosti raèunalnikov in mreže.

Z dajanjem storitev razliènim zraènim prevoznikom prisiljujejo letališko osebje na uporabo razliènih raèunalniških sistemov. To pomeni dnevno uporabo razliènih uporabniških vmesnikov kar otežuje delo in zvišuje stroške vadenja.

If the Basic Weight in the equation is replaced by the value for Dry Operating Weight (D.O.W.) with the appropriate position of the centre of gravity, then the obtained result is the Dry Operating Index - D.O.I. (Figure 3).

If the empty aircraft with the calculated basic or dry operating index is to be loaded and balanced, the index value has to be recalculated: new index = index of the empty aircraft + corrective index, or I (loaded 0 D. O. I. + DI), and the corrective index is:

(4),

where:

B is a constant, the same as for the calculation of the basic index;

Xrl is the distance from the manufacturer’s cross section to the index or reference line;

Xt is the distance of the centre of gravity of the cargo (loaded in the aircraft) from the manufacturer’s cross section; Gt is the weight of the loaded cargo.

Results for the basic index (for every aircraft type separately) are standard, and every airline determines these individually. The value of the Dry Operating Weight depends on the number and weight of the crew members, the weight of food and beverages for the passengers and crew (catering), the weight of the Duty Free Shop goods, and these are presented in a table [1].

The reference or index line can be set anywhere on the aircraft (depending on for which cargo the large influence of the resulting moment or index needs to be eliminated), so that there may be different index values for the same aircraft type.

2 PROBLEMS WITH EXISTING AIRLINE BALANCING PROGRAMS

Airlines normally have their own systems for aircraft balancing. This makes problems for the airport staff in load control, i.e., aircraft balancing. Similar programs have been developed exclusively by big air carriers, e.g., Lufthansa, British Airways, Swissair, Delta, mainly for their own needs and according to their own criteria and standards. These programs are later sold to other air carriers, who are provided with their own program support. Therefore, they avoided using graphical support, both because of the large amount of memory required, and because of the relatively low speed and computer and network capacity, available some ten years ago.

Furthermore the offering of services to different air carriers, forces airport staff to use different computerised systems. That means the daily use of different user interfaces, which makes work significantly more difficult, and increases training costs.

(Xrl Xt Gt) I

-3 RAÈUNALNIŠKI PROGRAM ZA URAVNOTEŽENJE LETALA

Raèunalniški program za uravnoteženje letala, ki so ga razvili na latelišèu Split, je tehnološko zamišljen tako, da uporablja isti vmesnik, lahko pa se uporablja za razliène zraène prevoznike in popolnoma ohranja njihove posebne standarde.

Glavne znaèilnosti programa za uravnoteženje letala so:

- program je namenjen za delo na osebnem raèunalniku v operativnem okolju in grafiènem vmesniku Windows 95, 98, NT, 2000, XP. Osebni raèunalniki so povezani z Windows 2000 raèunalniškim omrežjem 4, 11. Slike na zaslonu so izdelane za monitorje z diagonalo 15 palcev, loèljivostjo 800×600 toèk in 4 bitne palete barv; - najpomembnejša znaèilnost programa je grafièni

diagram za vsak tip letala, ki omogoèa balanserju letala, da vidi v vsakem trenutku, kje je težišèe letala;

- program omogoèa hkrati delo številnim uporabnikom, ki uravnotežijo razlièna letala. Vnos podatkov o številu in masi potnikov, prtljage in tovora je avtomatiziran. Prav tako tudi pošiljanje vseh poroèil v zvezi z nakladanjem in uravnoteženjem letala;

- glede na to, da so narejeni posebni moduli, baze in grafièni diagrami za vsak tip letala za vse zraène prevoznike, je program izdelan tako, da je mogoèe dopolnjevanje z novimi tipi letal brez omejitve;

- varnost programa mora biti najveèja zaradi velikega števila baz, indeksov in podatkov, ki se za vsak let shranjujejo v posebnem delovnem prostoru, direktoriju, na trdem disku;

- program je izdelan v programskem jeziku Fox Pro 2,6a, jeziku, ki je eden od nareèij jezika Xbase, namenjen pa je delu z bazami podatkov;

- ker se program za uravnoteženje letala sproži iz glavnega programa za avtomatizacijo dejavnosti sprejema in odpreme letala, potnikov in tovora, je ta naèin dela programa modularen, kar pomeni, da so v delovnem pomnilniku raèunalnika hkrati dejavni najveè štirje moduli. Delovni pomnilnik (RAM) je najbolj razbremenjen, zato je hitrost programa veèja, ostaja pa dovolj prostora za hkratno delo drugih programov;

- da bi lahko program delal usklajeno s postavljenimi zahtevami, obstaja nekoliko preglednic, v katerih so organizirani najpomembnejši podatki o vsaki verziji in tipu letala vsakega zraènega prevoznika.

4 TEHNOLOŠKO DELOVANJE

Raèunalniški program za uravnoteženje letala ima širok spekter možnosti na razliènih

3 COMPUTER PROGRAM FOR AIRCRAFT BALANCING

The computer program for aircraft balancing developed at Airport Split is technologically conceived in a manner that, although using the same users interface, it may be applied to different carriers, entirely respecting their particular standards.

The basic characteristics of the program for aircraft balancing are as follows:

- the program is intended to work on PCs in the operating environment and graphical interface of Windows 95, 98, NT, 2000, XP. The PCs are connected to the Windows 2000 computer network 4, 11. The images on the screen are meant for monitors of diagonal size 15 inches, resolution 800×600 pixels, and a 4-bit colour palette;

- the most important characteristic of the program is the graphical diagram for every single aircraft type, which allows the aircraft load controller to be able to see at any moment where the centre of gravity is; - the program allows the simultaneous work of a number

of users who perform the balancing of different aircraft, and the input of data about the number and weight of the passengers and cargo, as well as loaded goods, and the sending of all messages related to loading and balancing the aircraft is automated;

- since special modules, bases and graphical diagrams are made for every aircraft type, of every single air carrier, the program has been developed in such a way that it can be supplemented by new types of aircraft, free of limitations;

- in order to ensure the maximum safety of program operation, and having in mind the large number of bases, indexes, and the need to keep the data, etc. the data about every flight are stored in a special directory on a hard disc; - the program has been developed in Fox Pro 2,6a,

i.e., a language that represents one of the Xbase dialects, intended for work with databases; - since the program for aircraft balancing gets activated

from the main program for automating aircraft, passengers and cargo handling activities, the program operates in a modular way, which means that a maximum of up to four modules are simultaneously active in the PC RAM. Thus, the operating load on the RAM is minimized, which allows much greater speed of the program, leaving enough room for the simultaneous running of other programs;

- in order to make the program work in compliance with the set requirements, a whole series of tables has been created that provide an organised set of the most important data about single versions and types of aircraft owned by single operators.

4 TECHNOLOGICAL FUNCTIONALITY

vari-zaslonih:

- za izbiro doloèenega letala, - prikaz mase,

- osnovni raèunalniški program,

- z najpomembnejšimi podatki, potrebnimi za uravnoteženje letala,

- za vpis gesla, kadar se spreminjajo vpisani podatki na zaslonu z vsemi najpomembnejšimi podatki, - prikaz mas z odprtimi polji za vpis potnikov, prtljage,

blaga in pošte,

- za vpis stvarne oddane mase in roène prtljage, - za vpis skupnega števila potnikov po sekcijah v

letalu,

- z grafiènim diagramom uravnoteženja letala, - možnost raèunalniškega programa, da svetuje

idealno uravnoteženost letala, - pregled dejanskih in najveèjih mas, - pregled podatkov o potnikih, - pregled podatkov o gorivu,

- vsebina poroèila o vkrcanih potnikih in natovorjenem tovoru,

- obrazec za obremenitev in uravnoteženost letala, - prikaz potniške kabine in zasedenih sedežev, - prikaz registriranih potnikov in tistih, kimanjkajo, - prikaz zasedenih sedežev,

- prikaz podatkov o registriranem tovoru za doloèen let itn.

5 SKLEP

Raèunalniški program je narejen uporabniku kar najbolj prijazno in je prilagojen obièajnim metodam dela, ki so bile že prej uporabljene, kar je bistveno skrajšalo vsakodnevno uporabo. Poglavitna razlika tega raèunalniškega programa za uravnoteženje letala in drugih, podobnih, je:

a. grafièni diagram, na katerem je v vsakem trenutku mogoèe vidno preveriti lego toèke težišèa letala v razliènih kritiènih trenutkih leta,

b. prilagojenost programa vseh tipov letal vseh zraènih prevoznikov v skladu z njihovimi standardi. Z drugimi besedami uporabnikom tega programa je omogoèeno, da za vsakega prevoznika posebej izdelajo bazo podatkov za vsak tip letala v skladu s prevoznikovimi operativnimi masami.

Problem grafiènega prikaza je, da se mora zaradi spremembe operativnih mas zamenjati (to zraèni prevozniki obèasno delajo), za to pa je pooblašèen samo avtor raèunalniškega programa. Da bi bili prihodnji uporabniki programa èim bolj samostojni, so razvili dinamièni grafièni diagram, na katerem so dovoljene meje ustrezajoèih najveèjih mas, ki se zamenjajo avtomatièno v skladu s spremembo numeriènih vrednosti. Tak diagram

ous screens:

- for selecting appropriate aircraft, - displaying weights,

- home screen of the computer programme, - with the most important data necessary for aircraft

balancing,

- requiring password when changing the entered data on the screen displaying all the most important data, - displaying weights with open boxes for the input

of passenger, baggage, cargo and mail,

- for the input of the actual weight of checked and cabin baggage,

- containing the total number of passengers per air-craft section,

- with a graphical diagram showing aircraft balance, - the possibility of a computer program to suggest

the ideal aircraft balance,

- viewing actual and maximum weights, - viewing data about passengers, - viewing data about fuel,

- content of the message about the passengers and cargo onboard,

- showing the passenger cabin layout and the occu-pied seats,

- showing the number of checked passengers and those missing,

- showing the seats occupied by passengers who have boarded the aircraft,

- overview of data regarding cargo checked for a particular flight, etc.

5 CONCLUSION

The computer program has been made as user-friendly as possible and adapted to the usual methods of work applied previously, which has made the final acceptance and everyday use of this program much easier to implement. The basic difference of the program for aircraft load and trim control developed at Airport Split and other similar programs lies in the following: a. the existence of a graphical diagram allowing a

visual check at any time of the aircraft’s centre of gravity in different critical moments of flight, b. the adaptability of the program to any aircraft type

of any air carrier in compliance with its standards. In other words, the users of this program can de-velop for every air carrier a separate database of every aircraft type in accordance with the carri-er’s specific operating weights.

appropri-je zdaj izdelan za vse tipe letal, ki pristajajo na hrvaških letališèih v Splitu, Dubrovniku, Pulju, Zadru, Osijeku in Knocku na Irskem.

Na koncu je treba poudariti, da je z uporabo raèunalniškega programa zelo poveèana natanènost izraèuna, s tem pa stabilnost in varnost letala v èasu leta. Èas, ki je potreben za izdelavo obrazca za obremenitev in uravnoteženost, je skrajšan od povpreèno deset minut, kolikor potrebuje za roèno izdelavo, na samo eno do dve minuti. Tako ostane veè èasa za popoln in natanèen nadzor zaposlenim, ki delajo pri sprejemu in odpremi letala.

Raèunalniški program za uravnoteženje letal so testirali in odobrili strokovnjaki za uravnoteženje letal naslednjih zraènih prevoznikov: Croatia Airlines, Adria Airways, Austrian Airlines, ÈSA, LOT, Malev, Lauda Air, Air Loyd, Fischer Air, Condor in Duo Airways. Air Zimbabwe uporablja ta program za uravnoteženje svojih letal.

ate maximum weights are changed automatically in ac-cordance with the modification of numerical values. Such a diagram has now been developed for all types of aircraft flying to the Croatian airports in Split, Dubrovnik, Pula, Zadar, Osijek and Knock, in Ireland.

Finally, it has to be pointed out that by us-ing this computer program the accuracy of the calcu-lation has been significantly improved, including also better stability and aircraft safety during flight. The duration necessary for completing the Load and Trim Sheet has been shortened from the ten minutes on average required to do this manually, to one to two minutes, thus leaving time for complete and precise control of staff working on unloading / loading of baggage and cargo, and total aircraft handling.

This computer program for aircraft balanc-ing has been tested and approved by the experts on aircraft balancing of the following air carriers: Croatia Airlines, Adria Airways, Austrian Airlines, CSA, LOT, Malev, Lauda Air, Air Lloyd, Fischer Air, Condor and Duo Airways. Air Zimbabwe is also using this bal-ancing program.

6 LITERATURA 6 REFERENCES

[1] Košèak, B. (1978) Osnovi aerodinamike, Obrazovni centar zraènog saobraæaja, Zagreb. [2] Airport handling manual, 19th _{Edition 1. January 1999.}

[3] Ashford, N., H.P.M. Stanton, A.C. Moore (1997) Airport operations, McGraw-Hill New York USA.

Authors’s Addresses: Prof.Dr. Stanislav Pavlin Faculty of Transport and Traffic Engineering Vukeliæeva 4

10000 Zagreb, Croatia [email protected]

Dr. Slavko Roguljiæ Zraèna luka Split-Kaštela Dr. Franje Tuðmana 96 Kaštela

21120 Split, Croatia

[email protected]

Prejeto: 12.2.2004 Sprejeto: 18.6.2004 Odprto za diskusijo: 1 leto Received: Accepted: Open for discussion: 1 year

Naslova avtorjev:prof.dr. Stanislav Pavlin Fakultet prometnih znanosti Vukeliæeva 4

10.000 Zagreb, Hrvatska [email protected]

dr. Slavko Roguljiæ Zraèna luka Split-Kaštela Dr. Franje Tuðmana 96 Kaštela

21120 Split, Hrvatska